Yahoo Tuning Groups Ultimate Backup tuning Gene's Bonehead 31-et notation

Gene,

If you add B##, why not also Cbb?

Regards,
Yahya

-----Original Message-----
________________________________________________________________________
Date: Tue, 05 Apr 2005 16:28:48 -0000
From: "Gene Ward Smith"
Subject: Re: Gene's Bonehead 31-et notation

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> This is intended to allow someone to explain how to sequence meantone
> music in Scala without getting too weird; I'm proposing it be added to
> Scala's notation systems file. Any emendations?

My own emendation would be this, if it works. Should it be B##, or
should we just skip that one?

0: C
1: Dbb B##
2: C#
3: Db
4: C##
5: D
6: Ebb
7: D#
8: Eb
9: D## Fbb
10: E
11: Fb
12: E#
13: F
14: Gbb E##
15: F#
16: Gb
17: F##
18: G
19: Abb
20: G#
21: Ab
22: G##
23: A
24: Bbb
25: A#
26: Bb
27: A## Cbb
28: B
29: Cb
30: B#
31: C

________________________________________________________________________

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🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
> Gene,
>
> If you add B##, why not also Cbb?

Why not indeed? Here's the new offical notation system, which Manuel
has given the dignified name of "Pythagoren" to, in place of "Bonehead".

0: C
1: Dbb Bx
2: C#
3: Db
4: Cx
5: D
6: Ebb
7: D#
8: Eb
9: Dx Fbb
10: E
11: Fb
12: E#
13: F
14: Gbb Ex
15: F#
16: Gb
17: Fx
18: G
19: Abb
20: G#
21: Ab
22: Gx
23: A
24: Bbb
25: A#
26: Bb
27: Ax Cbb
28: B
29: Cb
30: B#
31: C

As you see, note 27 is both Ax and Cbb. I'm going to put up a page now
explaining to people how they can compose in meantone, and pointing
out that they probably already do, more or less. Of course the really
scary thing is that now C-Ex-A# is a perfectly feasible chord, and
etc. One great feature about 31-et is that it settles the vexing
question of whether Ex or Gbb is the proper 11/8 by making them
enharmonic equivalents.

🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com,
"Gene Ward Smith" <gwsmith@s...> wrote:

> --- In tuning@yahoogroups.com,
> "Yahya Abdal-Aziz" <yahya@m...> wrote:
> >
> > Gene,
> >
> > If you add B##, why not also Cbb?
>
> Why not indeed? Here's the new
> offical notation system, which Manuel
> has given the dignified name of
> "Pythagoren" to, in place of "Bonehead".
>
> 0: C
> 1: Dbb Bx
> 2: C#
> 3: Db
> 4: Cx
> 5: D
> 6: Ebb
> 7: D#
> 8: Eb
> 9: Dx Fbb
> 10: E
> 11: Fb
> 12: E#
> 13: F
> 14: Gbb Ex
> 15: F#
> 16: Gb
> 17: Fx
> 18: G
> 19: Abb
> 20: G#
> 21: Ab
> 22: Gx
> 23: A
> 24: Bbb
> 25: A#
> 26: Bb
> 27: Ax Cbb
> 28: B
> 29: Cb
> 30: B#
> 31: C
>
> As you see, note 27 is both Ax and Cbb. I'm going to put up a page now
> explaining to people how they can compose in meantone, and pointing
> out that they probably already do, more or less. Of course the really
> scary thing is that now C-Ex-A# is a perfectly feasible chord, and
> etc. One great feature about 31-et is that it settles the vexing
> question of whether Ex or Gbb is the proper 11/8 by making them
> enharmonic equivalents.

this can be seen graphically on the
Tonalsoft Encyclopedia "meantone" entry:

http://tonalsoft.com/enc/meantone.htm

about 1/3 of the way down the page, under
the heading "meanpop/huygens" ... there's
a mouse-over applet which shows each of those
two mappings of 11 in cyan (light blue) for
the whole meantone spectrum (family).

there are several vertical linear plots on
that graph which are not labeled (and should be),
which represent particular meantone tunings.
one is made of green plus signs, right at the
point on the x-axis labeled "-0.25", and represents
1/4-comma meantone. another, just to the right of
that one, is a vertical line of black dots which
represents 31-edo.

by mousing over the "meanpop" and "huygens" links
(without clicking), you can see the mappings of the
4 prime factors for all the meantones. the only
one which changes between the two is that of
prime-factor 11 (in cyan) -- and it can be seen
that the point where the two mappings intersect
is right at 31-edo.

incidentally, 31-edo page

http://tonalsoft.com/enc/31edo.htm

has an explanation of the mathematics of the
small intervals (anomalies) in 31-edo, and a
graphic of the 31-edo circle-of-5ths which
shows the enharmonic equivalence at Ax/Cbb
and Ex/Gbb;

and my 1/4-comma-meantone page

http://tonalsoft.com/enc/1-4cmt.htm

shows how, starting with "C" as the reference,
extending the 1/4-comma meantone chain-of-5ths,
in a way which is logically based on standard
notation, results in enharmonic equivalence at
exactly the same pitch-classes noted by Gene:
namely, Ax and Cbb.

but why would 31-edo be dubbed "Pythagorean"?
that doesn't seem to make sense to me, for a
meantone tuning.

-monz

🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> this can be seen graphically on the
> Tonalsoft Encyclopedia "meantone" entry:
>
> http://tonalsoft.com/enc/meantone.htm
>
> about 1/3 of the way down the page, under
> the heading "meanpop/huygens" ... there's
> a mouse-over applet which shows each of those
> two mappings of 11 in cyan (light blue) for
> the whole meantone spectrum (family).
>
> <snip>
>
> by mousing over the "meanpop" and "huygens" links
> (without clicking), you can see the mappings of the
> 4 prime factors for all the meantones. the only
> one which changes between the two is that of
> prime-factor 11 (in cyan) -- and it can be seen
> that the point where the two mappings intersect
> is right at 31-edo.

oops, my bad ... i meant to say that the graph shows
the *error* of the mappings of the prime-factors
(in cents), *not* the mappings themselves. sorry.

-monz

🔗Kraig Grady <kraiggrady@anaphoria.com>

When i worked with 31 . using + and - were no problem at all . Easier and less cluttered than double sharps and flats and all you notes with the same letter name were quite close to each other
C,C+, C#
Db, D-, D
Fokker proposed half sharps and half Flats but the latter doesn't use a symbol on the typewriter. Pluses and minus are easier to read quickly.
Anyways the below is pretty much covered on page 3 of http://www.anaphoria.com/xen2.PDF >>tions?
>> >>
>
>My own emendation would be this, if it works. Should it be B##, or
>should we just skip that one?
>
> 0: C
> 1: Dbb B##
> 2: C# > 3: Db
> 4: C##
> 5: D
> 6: Ebb
> 7: D# > 8: Eb
> 9: D## Fbb
> 10: E
> 11: Fb
> 12: E# > 13: F
> 14: Gbb E##
> 15: F# > 16: Gb
> 17: F## > 18: G
> 19: Abb
> 20: G# > 21: Ab
> 22: G## > 23: A
> 24: Bbb
> 25: A# > 26: Bb
> 27: A## Cbb
> 28: B
> 29: Cb
> 30: B# > 31: C
>
>________________________________________________________________________
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
>
> When i worked with 31 . using + and - were no problem at all . Easier
> and less cluttered than double sharps and flats and all you notes with
> the same letter name were quite close to each other
> C,C+, C#
> Db, D-, D

Yes, but you are a tuning person. I'm not trying to explain this to
the microtonal community, but to people with an ordinary musical
education, part of which is exposure to double sharps and flats. Using
double sharps and flats, we can get 35 notes of meantone, which means
we have enough notes to close the circle at 31, with a few enharmonic
equivalences left over. In other words, the ordinary musical notation
we see in score suffices to note 31-equal. That being so, someone with
no knowledge of tuning can dive right in to 31. Of course the point of
view they will then have on 31 is a meantone point of view, whereas 31
has other tricks up its sleeve, but clearly meantone is the place to
start.

🔗Rich Holmes <rsholmes@mailbox.syr.edu>

Kraig Grady <kraiggrady@anaphoria.com> writes:

> When i worked with 31 . using + and - were no problem at all . Easier
> and less cluttered than double sharps and flats and all you notes with
> the same letter name were quite close to each other
> C,C+, C#
> Db, D-, D

Though if working with diatonic scales, this obscures the
relationships between notes in some of the keys, e.g. the notes of G#
major are

G# A# B# C# D# E# Fx G#

in the scheme Gene wrote about; in yours it's

G# A# B# C# D# E# G- G#

making the major seventh from the tonic a notational flattened unison.
(By some people's definitions, as discussed recently, this would fail
to qualify as a diatonic scale, since it lacks an F!) Indeed, there
would be no key signature that represents G# major in your scheme.

I suppose this isn't an issue for e.g. atonal 31-ET music, though.

- Rich Holmes

🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com,
"Gene Ward Smith" <gwsmith@s...> wrote:

> --- In tuning@yahoogroups.com,
> Kraig Grady <kraiggrady@a...>
> wrote:
> >
> > When i worked with 31 .
> > using + and - were no problem
> > at all . Easier and less
> > cluttered than double sharps
> > and flats and all you notes
> > with the same letter name were
> > quite close to each other
> > C,C+, C#
> > Db, D-, D
>
> Yes, but you are a tuning person.
> I'm not trying to explain this to
> the microtonal community, but to
> people with an ordinary musical
> education, part of which is
> exposure to double sharps and
> flats. Using double sharps and
> flats, we can get 35 notes of
> meantone, which means we have
> enough notes to close the circle
> at 31, with a few enharmonic
> equivalences left over. In other words, the ordinary musical
> notation we see in score suffices to note 31-equal. That being
> so, someone with no knowledge of tuning can dive right in
> to 31. Of course the point of view they will then have on 31
> is a meantone point of view, whereas 31 has other tricks up
> its sleeve, but clearly meantone is the place to start.

i agree. and BTW, standard practice among musicians is
to notate double-sharps with the little "x" rather than
with two sharp symbols ... ## is found too, but is less common.

-monz

🔗Kraig Grady <kraiggrady@anaphoria.com>

Hello Rich!
' In 31 equal there are so many possible scales that whether one has G# Major misses the point. Far from what i did in 31 being atonal, nor were there parties in the Dutch school leaning this way had trouble with such a notation. Also Jonathan Glasier used this same notation in San diego. One gets used to + and - very very quickly as those who used Fokkers notation did likewise. There is nothing that prevents one from using a double sharp, and in certain cases i would use them. In fact when i used a 22 tone vibraphone tuned to the eikosany, since i also had a 31 tone marimba that overlapped in tones i used the 31 tone notation which appeared a bit akward at first but served my use over 15 years.
I can't imagine a 31 tone composer being tied to the diatonic , and the music that has been writtenin 31 bares this out.

> From: Rich Holmes<rsholmes@mailbox.syr.edu>
>Subject: Re: Gene's Bonehead 31-et notation
>
>Kraig Grady <kraiggrady@anaphoria.com> writes:
>
> >
>>> When i worked with 31 . using + and - were no problem at all . Easier >>> and less cluttered than double sharps and flats and all you notes with >>> the same letter name were quite close to each other
>>> C,C+, C#
>>> Db, D-, D
>> >>
> Though if working with diatonic scales, this obscures the > relationships between notes in some of the keys, e.g. the notes of G# > major are G# A# B# C# D# E# Fx G# in the scheme Gene wrote about; in > yours it's G# A# B# C# D# E# G- G# making the major seventh from the > tonic a notational flattened unison. (By some people's definitions, as > discussed recently, this would fail to qualify as a diatonic scale, > since it lacks an F!) Indeed, there would be no key signature that > represents G# major in your scheme. I suppose this isn't an issue for > e.g. atonal 31-ET music, though. - Rich Holmes > ________________________________________________________________________

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗Kraig Grady <kraiggrady@anaphoria.com>

As i pointed out in my other post this notation has worked fine for those who knew little about theory. Emil richards also used it and you can ask Glasier , who exposed it to a myriad of
non tuning specialist if there was a problem.
Nothing is more confusing to me is when you have letter names crossing if we are going to talk about the layman, to have c higher than Ds especially in a meantone system just makes it hard to find where your notes are. Also put it on a keyboard and see where it lies. Double flats are a mess and + and - couldn't be simpler that saying between a natural and a sharp you have a plus and between a natural and a flat you have a minus.
No one who i ever showed this to had a problem and this often was to people who were against the idea of microtones at the time. Universally without exception NO ONE objected to the notation.

Here we are back invented the wheel

Message: 5 Date: Thu, 07 Apr 2005 18:23:22 -0000
From: "monz" <monz@tonalsoft.com>
Subject: Re: Gene's Bonehead 31-et notation

--- In tuning@yahoogroups.com,
"Gene Ward Smith" <gwsmith@s...> wrote:
>
>> >> Yes, but you are a tuning person.
>> I'm not trying to explain this to
>> the microtonal community, but to
>> people with an ordinary musical
>> education, part of which is >> exposure to double sharps and >> flats. Using double sharps and >> flats, we can get 35 notes of
>> meantone, which means we have
>> enough notes to close the circle
>> at 31, with a few enharmonic
>> equivalences left over. In other words, the ordinary musical
>> notation we see in score suffices to note 31-equal. That being
>> so, someone with no knowledge of tuning can dive right in
>> to 31. Of course the point of view they will then have on 31
>> is a meantone point of view, whereas 31 has other tricks up
>> its sleeve, but clearly meantone is the place to start.
> >

i agree. and BTW, standard practice among musicians is
to notate double-sharps with the little "x" rather than
with two sharp symbols ... ## is found too, but is less common.

-monz

> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗Rich Holmes <rsholmes@mailbox.syr.edu>

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:

> As i pointed out in my other post this notation has worked fine for
> those who knew little about theory.

I'm writing that page for people who may know a *lot* about theory,
meaning the theory of the common practice music of the Western
tradition. People who start from the diatonic scale and work up from
there.

> Nothing is more confusing to me is when you have letter names crossing
> if we are going to talk about the layman, to have c higher than Ds
> especially in a meantone system just makes it hard to find where your
> notes are.

They don't need to find where the notes are, since this has nothing to
do with keybaords.

> Here we are back invented the wheel

This wheel has already been invented. It is the old wheel people who
are not microtonalists are already rolling around on. It strikes me as
absurd to tell someone interested in using 31-equal to write
common-practice style music that they now must use some new, goofball
wheel which will not make any sense to them. Why not simply make use
of the standard notation which has been around for hundreds of years,
and *which they already know*?

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Hi Rich,

The more I think about the issue, the more I'm convinced that a
diatonic scale is one, _however notated_, in which _melodic_
movement within tetrachords is "dia tonoi" - "through the tones"
- as far as possible. Which means that each tetrachord will need
to ascend by two "major" steps of a tone, and one "minor" step of
a semitone to reach the perfect fourth from the root. Any diatonic
scale balanced between utonal and otonal will have two tetrachords,
one with the root as its starting point and the other with the root
as the end point.

So calling a note Fx or G- doesn't change the intervals that the
scale comprises. I think it's merely a practical consequence of a
scale's being a balanced diatonic scale that we _can_ notate it with
seven distinct letter names (four in each of two tetrachords, with
only one common letter name between them) - if we choose to do so.

Eg, a balanced diatonic scale might consist of the upper tetrachord
CDEF, and the lower tetrachord GABC, giving the scale GABCDEF.
(Note I don't consider it as CDEF + GABC, which gives eight notes
and makes assumptions about octave equivalence.) Starting a
semitone higher, we have the scale G#A#B#C#D#E#F#. Starting
a fifth higher still, we have D#E#FxG#A#B#C# - your scale, but
with the tonic in a different position than usual. Any notation that
requires us to write this scale with other than 7 letter names simply
obscures the relationships between the notes - that they are members
of a balanced diatonic scale. Accordingly, I do not see the sense in
writing this scale as D#E#G-G#A#B#C#. What would appear to be
a notational convenience makes it harder to understand the music.
A similar example occurred recently - as I was setting a friend's
jazz piece, I noticed that he had written out the chord name as B,
while the melody note was given as Gb, rather than F#! The fact that
the music then pivoted on the F#-Gb and modulated through a series
of flatted keys made it no less strange to see ...

Regards,
Yahya

-----Original Message-----
________________________________________________________________________
Date: 07 Apr 2005 14:17:57 -0400
From: Rich Holmes
Subject: Re: Gene's Bonehead 31-et notation

Kraig Grady <kraiggrady@an...> writes:

Though if working with diatonic scales, this obscures the
relationships between notes in some of the keys, e.g. the notes of G#
major are

G# A# B# C# D# E# Fx G#

in the scheme Gene wrote about; in yours it's

G# A# B# C# D# E# G- G#

I suppose this isn't an issue for e.g. atonal 31-ET music, though.

- Rich Holmes

________________________________________________________________________

🔗Rich Holmes <rsholmes@mailbox.syr.edu>

"Yahya Abdal-Aziz" <yahya@melbpc.org.au> writes:

> Hi Rich,
>
> The more I think about the issue, the more I'm convinced that a
> diatonic scale is one, _however notated_, in which ...

Sure. I cited the idea that a diatonic scale is one notated with each
of the letters from A through G, but I don't agree with it.

> Any notation that
> requires us to write this scale with other than 7 letter names simply
> obscures the relationships between the notes - that they are members
> of a balanced diatonic scale. Accordingly, I do not see the sense in
> writing this scale as D#E#G-G#A#B#C#. What would appear to be
> a notational convenience makes it harder to understand the music.

Right, just the point I was trying to convey.

- Rich Holmes

🔗Kraig Grady <kraiggrady@anaphoria.com>

As i stated, in this case there is no reason to notate it as such. 31 is no different than any other system where you can notate the same tone differently.
No notation ever 'requires' a note to be notated in a certain way. In 12 ET in C3 Major the note C is not required to be notated as such , even though if you ask any one out of context what note this is they will say C . although in this context you will notate it as B#.
When there is a body of 31 tone music that exceeds that which has already been done, possibly such a change might be profitable. If some ois so conservative that they are just interested in diatonic scales, i cannot imagine that why they would be interested in 31. once again those who have written real music in 31 tones have not shown any preferance for such scales. To propose that this is what people want seems to be ahistorical and theorical not based on any fact of what we have on hand.
I suggest one takes a composition by Hank Badings and see how this notation works in practice.

> From: Rich Holmes<rsholmes@mailbox.syr.edu>
>Subject: >Re: Re: Gene's Bonehead 31-et notation
>"Yahya Abdal-Aziz" <yahya@melbpc.org.au> writes:
>
> >
>>Hi Rich,
>>
>>The more I think about the issue, the more I'm convinced that a
>>diatonic scale is one, _however notated_, in which ...
>> >>
>
>Sure. I cited the idea that a diatonic scale is one notated with each
>of the letters from A through G, but I don't agree with it.
>
> >
>>Any notation that
>>requires us to write this scale with other than 7 letter names simply
>>obscures the relationships between the notes - that they are members
>>of a balanced diatonic scale. Accordingly, I do not see the sense in >>writing this scale as D#E#G-G#A#B#C#. What would appear to be
>>a notational convenience makes it harder to understand the music.
>> >>
>
>Right, just the point I was trying to convey.
>
>- Rich Holmes
>
>
>
>________________________________________________________________________
>
>
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗Rich Holmes <rsholmes@mailbox.syr.edu>

Kraig Grady <kraiggrady@anaphoria.com> writes:

> If some
> ois so conservative that they are just interested in diatonic scales, i
> cannot imagine that why they would be interested in 31.

First, what makes you think this is an issue only for people who are
interested ONLY in diatonic scales? Some people are interested in
diatonic scales AND other sorts of scales, and will want to notate
each in an appropriate way. And it is not only in diatonic music that
one will (usually) benefit from notation that makes intervallic
relationships clear.

Second, there ARE people on this list who have said they're interested
in diatonic scales in 31-ET. Evidently you haven't been listening.
And there is Blackwood, who wrote a book about diatonic tunings,
including 31-ET.

Third, what makes you think my comment was intended to apply to all
31-ET composers in all circumstances? If you need a notation for
31-ET but do not need to convey to a reader the perfect fifth nature
of the interval from B# to F##, notating the latter note as G- is a
perfectly reasonable thing to do. Just be aware of what is being
obscured thereby.

Finally, to suggest that because all the 31-ET music you are familiar
with has certain attributes, therefore all 'real' composers of 31-ET
music should and will write music with those attributes, is arrogant,
condescending, and naive.

- Rich Holmes

🔗monz <monz@tonalsoft.com>

hi Kraig, Rich, Gene,

--- In tuning@yahoogroups.com, Rich Holmes<rsholmes@m...> wrote:
> Kraig Grady <kraiggrady@a...> writes:

> > If some ois so conservative that they
> > are just interested in diatonic scales,
> > i cannot imagine that why they would be
> > interested in 31.
>
> First, what makes you think this is an
> issue only for people who are
> interested ONLY in diatonic scales?
> <etc. -- snip>

why is there so much argument about this?

all Gene proposed is that, since so many
musicians are *already* familiar with the
way meantone works because standard musical
notation is based on it, if they want to
get into microtonality and are looking for
a "way in", notating 31-edo in its meantone
form would make the 31-edo pitches and intervals
easier to grasp since the intonational concepts
behind the notation are already familiar.

that seems entirely reasonable to me, and there's
also a strong historical precedent for it, since
advocacy of 31-edo initially arose within a
meantone context.

of course, if someone wants to use 31-edo in a
non-meantone way -- and there are many, since this
is such a useful tuning -- then by all means, use
a different notation ... i'm sure Fokker's would
serve very well in a lot of cases, and Erv's too.

but for a musician whose entire musical life has
been conditioned by 12-edo, using meantone notation
for 31 is a great way to start learning what
microtonality is about.

-monz

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:

> When there is a body of 31 tone music that exceeds that which has
> already been done, possibly such a change might be profitable.

It exists. It's called meantone music, and there is *far* more of it
than of any kind of microtonal 31 tone music. No comparison. Not even
close.

If some
> ois so conservative that they are just interested in diatonic scales, i
> cannot imagine that why they would be interested in 31.

Because like so many people for several *centuries* of musical
practice, they might like to listen to music in better tune than 12-et
supplies.

once again those
> who have written real music in 31 tones have not shown any preferance
> for such scales.

This is kind of insulting to the many great composers who wrote in a
meantone tuning, isn't it? Since when did they get demoted to musical
dunce status?

To propose that this is what people want seems to be
> ahistorical and theorical not based on any fact of what we have on hand.

Ahistorical?? What in the world are you talking about? Tell me,
please, your version of the history of Western tuning systems.

> I suggest one takes a composition by Hank Badings and see how this
> notation works in practice.

I suggest you take a composition by Josquin Despres, Claudio
Monteverdi, Francois Couperin, or J. C. Bach and see how this notation
works in practice.

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:

> why is there so much argument about this?

Because this is the Internet.

> all Gene proposed is that, since so many
> musicians are *already* familiar with the
> way meantone works because standard musical
> notation is based on it, if they want to
> get into microtonality and are looking for
> a "way in", notating 31-edo in its meantone
> form would make the 31-edo pitches and intervals
> easier to grasp since the intonational concepts
> behind the notation are already familiar.

Actually, I'm being a little sneakier than that. I find there are
people who are quite open to the idea of tuning the kind of music they
already like and write in meantone, since they find, when I show them
the comparison, that they prefer the sound. If they get sucked into
microtonality as a consequence, that would be fine by me. If they
don't, I still will be able to listen to what they write with more
pleasure. Some of these people are so conservative there is basically
no chance of that happening, but with others, who knows?

🔗Ozan Yarman <ozanyarman@superonline.com>

I have personally been considering 31-ET not only for diatonical genera in maqam music, but also for other possible and exciting applications in microtonal practice, historical, Western or otherwise. I am in alignment with Gene, Rich and Monz on this one.

Cordially,
Ozan

----- Original Message -----
From: Rich Holmes
To: tuning@yahoogroups.com
Sent: 11 Nisan 2005 Pazartesi 20:49
Subject: Re: [tuning] Re: Re: Gene's Bonehead 31-et notation

Kraig Grady <kraiggrady@anaphoria.com> writes:

> If some
> ois so conservative that they are just interested in diatonic scales, i
> cannot imagine that why they would be interested in 31.

- Rich Holmes

🔗Maximiliano G. Miranda Zanetti <giordanobruno76@yahoo.com.ar>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> >
> > When i worked with 31 . using + and - were no problem at all .
Easier
> > and less cluttered than double sharps and flats and all you
notes with
> > the same letter name were quite close to each other
> > C,C+, C#
> > Db, D-, D
>

I strongly disfavour the -/+ notation, Kraig, for it gets confused
with the -/+ I use for characterising intervals (eg. C E| = 3M+,
supermajor third. 5-, subperfect fifth,... I just take |,;,b,b; etc.
However, if you have a different notation for intervals, or just
care less about it, go for it.

> Yes, but you are a tuning person. I'm not trying to explain this to
> the microtonal community, but to people with an ordinary musical
> education, part of which is exposure to double sharps and flats.
Using
> double sharps and flats, we can get 35 notes of meantone, which
means
> we have enough notes to close the circle at 31, with a few
enharmonic
> equivalences left over. In other words, the ordinary musical
notation
> we see in score suffices to note 31-equal. That being so, someone
with
> no knowledge of tuning can dive right in to 31. Of course the
point of
> view they will then have on 31 is a meantone point of view,
whereas 31
> has other tricks up its sleeve, but clearly meantone is the place
to
> start.

In my humble opinion, Gene, for beginners it's just plain easy to
teach them to split a tone (C-D) in five diesis and a (diatonic)
semitone in three diesis, then show them the enharmonic spelling
equivalence. [I think] it's not that difficult. Most musicians just
learn f#=Gb in 12-et; without ever knowing about what meantone is
about, they could well dive into 31 et in this way.

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Maximiliano G. Miranda Zanetti <giordanobruno76@yahoo.com.ar>

🔗Kraig Grady <kraiggrady@anaphoria.com>

Kraig Grady <kraiggrady@anaphoria.com> writes:

This is what i said and i gave a rather simple example how this notation was not very desirable. i also suggested we translate a piece of 31 tone music into this notation and look at it. you pick it. Second, there ARE people on this list who have said they're interested
in diatonic scales in 31-ET. Evidently you haven't been listening.
And there is Blackwood, who wrote a book about diatonic tunings,
including 31-ET.

As i said in the cases in hand it might make sense to notate that way. although if you think that if one notates D# and Fx and you think someone will give you a 5/4 I would be quite surprised. not from a string player

One example and a shortfall of the tuning as you correctly point out. One points such animal out at the beginning and it is soon forgotten in practice, as someone who used it. If you take a a set of double sharps and flat you will eventually run across the very same problem Finally, to suggest that because all the 31-ET music you are familiar
with has certain attributes, therefore all 'real' composers of 31-ET
music should and will write music with those attributes, is arrogant,
condescending, and naive.

It is not 31 tone music that "i Am Familiar with" . It is the body of 31 tone music period unless there are some hidden stacks of the stuff somewhere. I did not propose that any composer write in a certain way. I said that composers so far have written a certain way and one of their problems was not notation for them or there performers.
The attributes you describe fits someone who has had not experience with the subject Arrogant- because they think those who use 31 tone haven't already noticed this notation. one of which i posted
condescending- in that what ever they did they didn't know as much as what proposed
naive- no experience with actually doing music in 31 tones

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗Kraig Grady <kraiggrady@anaphoria.com>

Hey Joe!
i think you are missing what is going on. Fokker and Wilson used a meantone notation, which as you point out what 31 tone is, what is being proposed is a pythagorean notation which as we all agree would be useful in certain rather limited circumstances

From: "monz" <monz@tonalsoft.com>
Subject: Re: Gene's Bonehead 31-et notation

hi Kraig, Rich, Gene,

--- In tuning@yahoogroups.com, Rich Holmes<rsholmes@m...> wrote:

>> Kraig Grady <kraiggrady@a...> writes:
> >
>>> > If some ois so conservative that they
>>> > are just interested in diatonic scales,
>>> > i cannot imagine that why they would be
>>> > interested in 31. >> >>
>> >> First, what makes you think this is an
>> issue only for people who are
>> interested ONLY in diatonic scales? >> <etc. -- snip>
> >
why is there so much argument about this? all Gene proposed is that, since so many musicians are *already* familiar with the way meantone works because standard musical notation is based on it, if they want to get into microtonality and are looking for a "way in", notating 31-edo in its meantone form would make the 31-edo pitches and intervals easier to grasp since the intonational concepts behind the notation are already familiar. that seems entirely reasonable to me, and there's also a strong historical precedent for it, since advocacy of 31-edo initially arose within a meantone context. of course, if someone wants to use 31-edo in a non-meantone way -- and there are many, since this is such a useful tuning -- then by all means, use a different notation ... i'm sure Fokker's would serve very well in a lot of cases, and Erv's too. but for a musician whose entire musical life has been conditioned by 12-edo, using meantone notation for 31 is a great way to start learning what microtonality is about. -monz

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗Kraig Grady <kraiggrady@anaphoria.com>

>
>
>> When there is a body of 31 tone music that exceeds that which has >> already been done, possibly such a change might be profitable.
> >

It exists. It's called meantone music, and there is *far* more of it
than of any kind of microtonal 31 tone music. No comparison. Not even
close.

To what the meantone composers who have written in meantone using the notation that worked fine for them.

If some >> ois so conservative that they are just interested in diatonic scales, i >> cannot imagine that why they would be interested in 31. > >

Because like so many people for several *centuries* of musical
practice, they might like to listen to music in better tune than 12-et
supplies.

once again those >> who have written real music in 31 tones have not shown any preferance >> for such scales.
> >

This is kind of insulting to the many great composers who wrote in a
meantone tuning, isn't it? Since when did they get demoted to musical
dunce status?

You are demoting absolutely 99% of the 31 tone composers before you as being ignorant of what meantone notation is. To propose that this is what people want seems to be >> ahistorical and theorical not based on any fact of what we have on hand.
> >

Ahistorical?? What in the world are you talking about? Tell me,
please, your version of the history of Western tuning systems.

Look at the scores of 31 tone miusc gene, look at Fokkers work and all the composers that actually wrote and performed 31 tone music. >> I suggest one takes a composition by Hank Badings and see how this >> notation works in practice.
> >

I suggest you take a composition by Josquin Despres, Claudio
Monteverdi, Francois Couperin, or J. C. Bach and see how this notation
works in practice.

These people did not approach the problem of 31 tone music. The entire dutch school as as well as the st. Loiuuis school and the west tcoast 31 practioners all knew these composers and did something else. Why do you think that is

________________________________________________________________________
________________________________________________________________________

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗Kraig Grady <kraiggrady@anaphoria.com>

________________________________________________________________________
________________________________________________________________________

Message: 9 Date: Mon, 11 Apr 2005 23:27:13 -0000
From: "Maximiliano G. Miranda Zanetti" <giordanobruno76@yahoo.com.ar>
Subject: Re: Gene's Bonehead 31-et notation

>
> >

I strongly disfavour the -/+ notation, Kraig, for it gets confused with the -/+ I use for characterising intervals (eg. C E| = 3M+, supermajor third. 5-, subperfect fifth,... I just take |,;,b,b; etc. However, if you have a different notation for intervals, or just care less about it, go for it.

just like sharps and flats mean different things in different tunings, one would expect = and - to sdo so also. there is also fokker notation

>>
>
In my humble opinion, Gene, for beginners it's just plain easy to teach them to split a tone (C-D) in five diesis and a (diatonic) semitone in three diesis, then show them the enharmonic spelling equivalence. [I think] it's not that difficult. Most musicians just learn f#=Gb in 12-et; without ever knowing about what meantone is about, they could well dive into 31 et in this way.

C C+ C# Db D- D
as opposed to
C Dbb C# Db CX D. 31 tone enharmnonic runs are going to look great

However, if you are thinking of musicians having knowledge of meantone evolution, your method would surely suffice for a start. But for tricks like Bb; 7/4, you may consider expanding the notation for future classes ;) There is much hypothetical suggestions that one is easier than the other, but the way such things are decided is in actual practice. + and - are good in the sense as they are easy to see if you are reading music. when you start using symbols on top of symbols thing get confusing. look above and see which is easier to read quickly

________________________________________________________________________
________________________________________________________________________

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗ambassadorbob <ambassadorbob@yahoo.com>

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:

> but for a musician whose entire musical life has
> been conditioned by 12-edo, using meantone notation
> for 31 is a great way to start learning what
> microtonality is about.

Hi guys,

As you say Joe, it seems quite reasonable, but I think the point
that Kraig may be getting at is an ideal of really breaking from 12-
edo and "common-practice", because at some point it really does
become a battle between entrenched "learning curves" and a creative
spirit.

Sometimes "reinventing the wheel" is the best and most necessary way
to go, in the interest of freedom. And to undo debilitating
abstractions, and the various ruts we're trained into from childhood.

I suspect, anyway, that general [musical?] knowledge is becoming so
degraded as to make it more likely that fewer and fewer alternatives
are being presented, in fact. So "conservative" arguments, like
music in general these days, fall on deaf ears, or simply help the
entrenched power structure remain so.

(Sorry if this is terribly OT, I haven't been following the
discussion very closely.)

But in general, I find the notation question a problem of that
nature, how to break the hegemony without burning down the house?

As long as one insists on using the vocabulary of common practice
theory, one is probably NOT really presenting an alternative to it.

Pete

🔗Kraig Grady <kraiggrady@anaphoria.com>

once again looking not only on page 3 of http://www.anaphoria.com/xen2.PDF
but also we can find a discussion of this notation in Fokkers New music in 31 tones, starting on page 35 we can see that both Fokker and Wilson came up with the bonehead notation . Fokker points out how poorly this notation deals with even notating the pure seventh used in the context of music. For those of you interested in the subject to pays to look a t what he says about the development of the notation that ended up being used. i am not aware of what Mandlebaum used for his 31 tone pieces also
Interesting I remember hearing some composition by Hans Kox and at the end of the Fokker book list a composition by him based on 3 and 7 in 1958, which Fokker does mention as a building block. Possibly this might be one of the earliest use of this. Mandlebaum does mention a Lursen (page 217 of multiple division....) who did short compositions along these lines
about 10 years earlier
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗monz <monz@tonalsoft.com>

hi Pete,

--- In tuning@yahoogroups.com, "ambassadorbob" <ambassadorbob@y...>
wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> > but for a musician whose entire musical life has
> > been conditioned by 12-edo, using meantone notation
> > for 31 is a great way to start learning what
> > microtonality is about.
>
> Hi guys,
>
> As you say Joe, it seems quite reasonable,
> but I think the point that Kraig may be
> getting at is an ideal of really breaking
> from 12-edo and "common-practice", because
> at some point it really does become a battle
> between entrenched "learning curves" and a
> creative spirit.
>
> Sometimes "reinventing the wheel" is the best and most necessary
> way to go, in the interest of freedom. And to undo debilitating
> abstractions, and the various ruts we're trained into from
> childhood.
>
> <snip>
>
> As long as one insists on using the vocabulary of common practice
> theory, one is probably NOT really presenting an alternative to it.

i agree with everything you said in your post. but, with
all due respect, i think that you and Kraig are both missing
Gene's point. as i understand it, Gene is simply encouraging
musicians with traditional training to finally *hear* what
the standard meantone notation has been notating all along.

maybe i understand and sympathize with Gene precisely because
of my extensive musical training ... in theory books, one
encounters meantone notation again and again and again, but
the author of the book invariably assumes that the music
being notated is tuned in 12-edo, which obliterates a lot
of what the notation specifies. and as we've come to learn
in our discussions on this list, the assumption of 12-edo
also obliterates a lot of what many composers intended their
music to sound like.

giving listeners the opportunity to hear common-practice
music actually tuned in 31-edo allows them to finally hear
the harmonic subleties that the meantone notation notates,
and which have always been missing from the 12-edo rendition.

and then the sneaky part of Gene's plan is that perhaps
some of those listeners will become intrigued by some of
the less familiar sounds available in 31-edo, and will be
encouraged to investigate that tuning further. at *that*
point, then they may become interested in, say, Fokker's
31-edo notation.

Gene's whole scheme is set up to introduce microtonality
to people who otherwise wouldn't be interested, or most
likely, wouldn't even be aware of its existence. those
here who are arguing against it are already so deeply
entrenched in the microtonal world that they're failing
to see his perspective.

-monz

🔗monz <monz@tonalsoft.com>

hi Kraig,

--- In tuning@yahoogroups.com,
Kraig Grady <kraiggrady@a...> wrote:

> Hey Joe!

a great song by one of my
favorite microtonal musicians!
(hee hee ...)

> i think you are missing
> what is going on. Fokker and
> Wilson used a meantone notation,
> which as you point out what
> 31 tone is, what is being
> proposed is a pythagorean
> notation which as we all agree
> would be useful in certain
> rather limited circumstances.

Gene's proposal is not pythagorean, it's straight-up meantone.
and as you point out, it's not something that he invented.
it goes all the way back to the early 1500's, when
1/4-comma meantone was first described. take a look
at my webpage on 1/4-comma meantone:

http://tonalsoft.com/enc/1-4cmt.htm

about halfway down, i have pitch-height graphs illustrating
the scales which are generated by the 1/4-comma meantone 5th.
you can see that when you reach a 32-tone scale (with "C"
as the reference, Cbb is -14 generators and Ax is +17),
there is a small interval between them of only ~6 cents:

generator period generator ~cents

-14 9 * [-14/4] 1047.902001 "Cbb"
17 - -9 * [ 17/4] 1041.833284 "Ax"
------------------------------
-31 18 * [-31/4] 6.068717548 (= ~6 & 1/15 cents)

= 1/4-comma meantone "quadruply-diminished 3rd"

(you'll have to click "Reply" on the stupid Yahoo interface
to see this correctly.)

this near-equivalence of 31-edo and 1/4-comma meantone
was noticed by Huygens back in the 1600's, and Huygens's
work is exactly what got Fokker interested in it.

so if one notates 1/4-comma meantone the usual way, one
ends up with something which is not too different from
31-edo in Gene's "boneheaded notation".

why do you call it "pythagorean"? simply because it uses
only sharps, flats, double-sharps, and double-flats as
accidentals? but it isn't pythagorean at all, it's pure
meantone.

-monz

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:

> Well if you run into problems you will have a host of other
composers who have actually written music in 31 tone (none of the above)

Anyone who's written music in meantone counts for the purposes of this
discussion. Anyone who has not does not. That is because we are
talking about a good notation of 31, using the fifth as a generator;
ie, using it in meantone.

> I suggest you try notating the scales with neutral thirds with what
they propose, or modulations in a cycle of fifths of any of your
classic chromatic and enharmonic tetrachords. I have done so and a
couple hundred other individuals have also

The composers I am talking about would not know a neutral third if it
ran up and bit them on the ear, *because* they come from a meantone
perspective. In fact, anyone used to a system where fifths are the
generators is likely to be shaky on neutral thirds.

Consequently, to work with neutral thirds it is more natural to choose
another temperament, in particular one where the neutral thirds are
generators. The question of notating neutral thirds is therefore not a
really live issue in an equal temperament being used for meantone. 31,
55, and 69 are meantone systems which all have them, but that does not
mean the interval is very significant in them when we are using the
division for meantone purposes.

🔗Pete McRae <ambassadorbob@yahoo.com>

monz <monz@tonalsoft.com> wrote:

> Gene's whole scheme is set up to introduce microtonality
to people who otherwise wouldn't be interested, or most
likely, wouldn't even be aware of its existence. those
here who are arguing against it are already so deeply
entrenched in the microtonal world that they're failing
to see his perspective.<

Yo, monz,

I hope you're right (on both counts? :-).

Cheers,

monz <monz@tonalsoft.com> wrote:

hi Pete,

--- In tuning@yahoogroups.com, "ambassadorbob"
wrote:
>
> --- In tuning@yahoogroups.com, "monz" wrote:
>
> > but for a musician whose entire musical life has
> > been conditioned by 12-edo, using meantone notation
> > for 31 is a great way to start learning what
> > microtonality is about.
>
> Hi guys,
>
> As you say Joe, it seems quite reasonable,
> but I think the point that Kraig may be
> getting at is an ideal of really breaking
> from 12-edo and "common-practice", because
> at some point it really does become a battle
> between entrenched "learning curves" and a
> creative spirit.
>
> Sometimes "reinventing the wheel" is the best and most necessary
> way to go, in the interest of freedom. And to undo debilitating
> abstractions, and the various ruts we're trained into from
> childhood.
>
>
>
> As long as one insists on using the vocabulary of common practice
> theory, one is probably NOT really presenting an alternative to it.

-monz

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🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Hi all,

Max wrote:
________________________________________________________________________
Date: Mon, 11 Apr 2005 23:27:13 -0000
From: "Maximiliano G. Miranda Zanetti" <giordano...>
Subject: Re: Gene's Bonehead 31-et notation

--------------8><-----Snip!

________________________________________________________________________

and later, replying to Gene:
________________________________________________________________________
Date: Tue, 12 Apr 2005 11:58:33 -0000
From: "Maximiliano G. Miranda Zanetti" <giordano...>
Subject: Re: Gene's Bonehead 31-et notation

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "Maximiliano G. Miranda Zanetti"
> <giordanobruno76@y...> wrote:
>
> > However, if you are thinking of musicians having knowledge of
> > meantone evolution, your method would surely suffice for a start.
> > But for tricks like Bb; 7/4, you may consider expanding the
notation
> > for future classes ;)
>
> These are traditionalists; I can just start talking about German
sixths.

Touchï¿½! :P

________________________________________________________________________

In my ever-more-humbled opinion, Max, I must still be more of a
beginner than I thought! :-)

So, would you please:
teach me how to split a tone (C-D) in five dieses and a (diatonic)
semitone in three dieses, then show me the enharmonic spelling
equivalence?

BTW, I'm perfectly happy to apply 31-tET to any style of music,
whether diatonic, atonal (if such a thing truly exists; I agree with
Monz that no music is devoid of harmonic, hence tonal, implications;
perhaps we're better off sticking to the term "serial"?) or microtonal.
I think that Kraig may have misunderstood me, and got the idea that
I wanted everyone to use 31-et for diatonic music to the exclusion of
microtonal music ... That was never my intention. If I could have
expressed myself more clearly, I would have. I would never knowingly
slight another's chosen mode of self-expression; even when it's not
my cup of tea, it may well be theirs ... and why should I start a storm
in their tea-cup?

Regards,
Yahya

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🔗Kraig Grady <kraiggrady@anaphoria.com>

Message: 11 Date: Tue, 12 Apr 2005 19:50:00 -0000
From: "Gene Ward Smith" <gwsmith@svpal.org>
Subject: Neutral third notation

I think you are assuming less of people than possibly thew case. I personally can't imagine an individual who might come from only a meantone background. except possibly some European folk music which can have the uncanny preservation of this in much of this music at times).
i woud assume that they would know what a seventh harmonic and even an eleventh, just from the fact that they are used in say jaxzz all the time atleast conceptionally. the neutral third comes up with the 11/9 which as you know quite good in this tuning. in fact the whole tradition of greek scales work quite well in this tuning, at least in giving the player an idea ( this was my first exposuse to these chords
and do not feel my time with 31 tone was wasted, in fact, it is one of the best tunings to tie in with the past as a gateway to the future. ) I resist the idea of pandering to the 'most conservative' method or transitions possible cause i belive this is what Yasser did and possible coming out the depression the idea of going from 12 to 31 was too much of an "expense" for those wanted to move forward. It would be interesting to see what Mandlebaum take on this would be since he met the man. There was nothing 'radical' about the dutch school or Fokker's approach which the same can be said of those at Webster College in St Louis

Suppose you are using n-equal, for an odd number n, in a temperament
in which the fifth is a generator, and where the number of steps to
get to a fifth is even. Such a system always has a neutral third,
since the number of steps to get to the fifth is even. Such a system
also *always* finds it maximally difficult to ever get to the neutral
third, whose complexity is as high as possible. The neutral third will
be 1/2 mod n, which represented by an integer will be (1-n)/2, or
-(n-1)/2. Hence in 31 it is -15 generator steps; in 41, -20; in 99,
-49; and in 171-equal it disappears completely over the horizon to
-85. The Incredible Retreating Neutral Third. Consequently, to work with neutral thirds it is more natural to choose
another temperament, in particular one where the neutral thirds are
generators. The question of notating neutral thirds is therefore not a
really live issue in an equal temperament being used for meantone. 31,
55, and 69 are meantone systems which all have them, but that does not
mean the interval is very significant in them when we are using the
division for meantone purposes.

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗Carl Lumma <ekin@lumma.org>

>The composers I am talking about would not know a neutral third if it
>ran up and bit them on the ear, *because* they come from a meantone
>perspective. In fact, anyone used to a system where fifths are the
>generators is likely to be shaky on neutral thirds.
>
> I think you are assuming less of people than possibly thew case. I
>personally can't imagine an individual who might come from only a
>meantone background. except possibly some European folk music which
>can have the uncanny preservation of this in much of this music at
>times).
> i woud assume that they would know what a seventh harmonic and even
>an eleventh, just from the fact that they are used in say jaxzz all
>the time at least conceptionally. the neutral third comes up with
>the 11/9 which as you know quite good in this tuning. in fact the
>whole tradition of greek scales work quite well in this tuning, at
>least in giving the player an idea (this was my first exposuse to
>these chords and do not feel my time with 31 tone was wasted, in fact,
>it is one of the best tunings to tie in with the past as a gateway
>to the future. )

Kraig, it sounds like Gene has infiltrated a group of neoclassical
composers somewhere on the internet. Even if they know what the 11th
harmonic is they probably are trying to avoid it!

-Carl

🔗Maximiliano G. Miranda Zanetti <giordanobruno76@yahoo.com.ar>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
>> However, if you have a different notation for intervals, or just
>> care less about it, go for it.
>
> just like sharps and flats mean different things in different
tunings, one would expect = and - to sdo so also.
> there is also fokker notation
>
> >>

...

> C C+ C# Db D- D
> as opposed to
> C Dbb C# Db CX D.
> 31 tone enharmnonic runs are going to look great
>
> However, if you are thinking of musicians having knowledge of
> meantone evolution, your method would surely suffice for a start.
> But for tricks like Bb; 7/4, you may consider expanding the
notation
> for future classes
> ;)
>
> There is much hypothetical suggestions that one is easier than the
other, but the way such things are decided is in actual practice. +
and - are good in the sense as they are easy to see if you are
reading music. when you start using symbols on top of symbols thing
get confusing. look above and see which is easier to read quickly
>

IMHO, Kraig,

C C| C# Db D; D

are not more difficult to read than

C C+ C# Db D- D

and, of course, constitute the standart view. Take me as a guy that
lives up to standards :D

Think for a second in rendering 4:5:6:7 and (4:5:6:7) in 31-edo. Do
you think C Eb G A+ is more straightforward than C Eb G Bbb? What
about C E G A# vs. C E G Bb;? That's why I prefer the broader
classical approach.

Anyway, take my posts as a statement on behalf of the traditional
scheme, rather than a disapproval of your view. You may feel free to
buy the brand you like most.

🔗Maximiliano G. Miranda Zanetti <giordanobruno76@yahoo.com.ar>

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
> Hi all,
>
> Max wrote:
>
_____________________________________________________________________
___
> Date: Mon, 11 Apr 2005 23:27:13 -0000
> From: "Maximiliano G. Miranda Zanetti" <giordano...>
> Subject: Re: Gene's Bonehead 31-et notation
>
> --------------8><-----Snip!
>
> In my humble opinion, Gene, for beginners it's just plain easy to
> teach them to split a tone (C-D) in five diesis and a (diatonic)
> semitone in three diesis, then show them the enharmonic spelling
> equivalence. [I think] it's not that difficult. Most musicians just
> learn f#=Gb in 12-et; without ever knowing about what meantone is
> about, they could well dive into 31 et in this way.
>
> However, if you are thinking of musicians having knowledge of
> meantone evolution, your method would surely suffice for a start.
> But for tricks like Bb; 7/4, you may consider expanding the
notation
> for future classes ;)
>
>
_____________________________________________________________________
___
>
...snip...
>
_____________________________________________________________________
___
>
> In my ever-more-humbled opinion, Max, I must still be more of a
> beginner than I thought! :-)
>
> So, would you please:
> teach me how to split a tone (C-D) in five dieses and a (diatonic)
> semitone in three dieses, then show me the enharmonic spelling
> equivalence?

Hi, Yahya! Sorry for a delayed answer. But I'm online when I'm
online! :P

The meaning of diesis in a 31-edo context is quite easy: Fist, think
of it as the thirty-oneth part of the octave (or is it thirty-
first?).

One point of 31-edo against, say, 22-edo, is that the diatonic
structure CDEFGAB can be straightforwardly defined: In 22-edo,
unison, major 2nd and mayor third's ideal representations are not
equally spaced, so the diatonic structure gets a little weird, if
not impossible to handle in a standard way. in 31-edo, however, you
get CDEFGAB's renderings as 0-5-10-13-18-23-28 31-edo steps.

It is not that you can't compose diatonic stuff in 22-edo, nor that
31-edo's approach can't be other than diatonic. It's just the fact
that 31-edo is diatonicly quite straightforward: one can notice that
the CDE...B scale is conformed by a mix of [uniform] large intervals
(tones) and small ones (diatonic semitone). Eg: tone C-D diatonic
semitone E-F.

So, take diesis defined as one step in 31-edo. A tone is then 5
diesis long, and a [diatonic] semitone is 3 diesis long. That is,
you get 5 steps between A and B (steps 23-28) and three diesis
between E and F (10-13). In other words, diesis is a 31-edo
equivalence for "semitone" used in the 12-edo scheme.

So, the five steps (dieses) between C and D, for instance, get named
as C| C# Db D; (| and ; are ASCII equivalences for the more
beautiful graphical semisharp and semiflat symbols).
Sesquisharps and sesquiflats [sesqui=prefix for "one and a half"]
can be written as #| and b; respectively. So, flat means "two dieses
lower in pitch", sharp "two dieses higher", semiflat "one diesis
lower", sesquisharp "three dieses higher", etc.

Then, C| is equivalent to Dbb, C# is equivalent to Db;, and so on.
The diatonic semitone (E-F) is divided as E E| F; F, or if you wish,
E Fb E# F.

If my explanation is not enough, the guys at the Huygens-Fokker
foundation have done a beautiful job at

http://www.xs4all.nl/~huygensf/english/index.html
(under "Theory")

There you can have a glimpse at the beautiful graphical symbols for
|, ;, etc.

As you may have noticed, Kraig has stated his preference for +/-
instead of |/;. Greg asked our opinion about the simplified scheme C
Dbb C# Db C## D.

> BTW, I'm perfectly happy to apply 31-tET to any style of music,
> whether diatonic, atonal (if such a thing truly exists; I agree
with
> Monz that no music is devoid of harmonic, hence tonal,
implications;
> perhaps we're better off sticking to the term "serial"?) or
microtonal.
> I think that Kraig may have misunderstood me, and got the idea that
> I wanted everyone to use 31-et for diatonic music to the exclusion
of
> microtonal music ... That was never my intention. If I could have
> expressed myself more clearly, I would have. I would never
knowingly
> slight another's chosen mode of self-expression; even when it's not
> my cup of tea, it may well be theirs ... and why should I start a
storm
> in their tea-cup?
>
> Regards,
> Yahya
>
Hum... Sunny weather is not frequent in this list :P

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Max wrote:
________________________________________________________________________

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
...
> So, would you please:
> teach me how to split a tone (C-D) in five dieses and a (diatonic)
> semitone in three dieses, then show me the enharmonic spelling
> equivalence?

Hi, Yahya! Sorry for a delayed answer. But I'm online when I'm
online! :P

[YA] No problem! Glad to have your answer - worth waiting for.

The meaning of diesis in a 31-edo context is quite easy: Fist, think
of it as the thirty-oneth part of the octave (or is it thirty-
first?).

[YA] Properly speaking, of course it's "thirty-first". But just for
the fun of speaking _improperly_, we will often say "thirty-oneth".
:-) At least this way, it is possible to find a rhyme for "month" -
a puzzle which has occupied many an English writer, from at least
the time of Ogden Nash. (He also lamented the lack of rhymes
for "orange" and "silver".)

Then, C| is equivalent to Dbb, C# is equivalent to Db;, and so on.
The diatonic semitone (E-F) is divided as E E| F; F, or if you wish,
E Fb E# F.

[YA] Thank you for an explanation of crystal clarity!

If my explanation is not enough, the guys at the Huygens-Fokker
foundation have done a beautiful job at

http://www.xs4all.nl/~huygensf/english/index.html
(under "Theory")

There you can have a glimpse at the beautiful graphical symbols for
|, ;, etc.

[YA] I'll look for them.

As you may have noticed, Kraig has stated his preference for +/-
instead of |/;. Greg asked our opinion about the simplified scheme C
Dbb C# Db C## D.

> BTW, I'm perfectly happy to apply 31-tET to any style of music,
> whether diatonic, atonal (if such a thing truly exists; I agree with
> Monz that no music is devoid of harmonic, hence tonal, implications;
> perhaps we're better off sticking to the term "serial"?) or microtonal.
> I think that Kraig may have misunderstood me, and got the idea that
> I wanted everyone to use 31-et for diatonic music to the exclusion of
> microtonal music ... That was never my intention. If I could have
> expressed myself more clearly, I would have. I would never knowingly
> slight another's chosen mode of self-expression; even when it's not
> my cup of tea, it may well be theirs ... and why should I start a storm
> in their tea-cup?
>
> Regards,
> Yahya
>
Hum... Sunny weather is not frequent in this list :P

[YA] Can't say I'd noticed ...! ;-)

________________________________________________________________________

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🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

> At least this way, it is possible to find a rhyme for "month" -
> a puzzle which has occupied many an English writer, from at least
> the time of Ogden Nash. (He also lamented the lack of rhymes
> for "orange" and "silver".)

From the Ganges to the Blornge
Walked the Raja every month
Chewing on an orange
And reading from his Grunth

> One point of 31-edo against, say, 22-edo, is that the diatonic
> structure CDEFGAB can be straightforwardly defined: In 22-edo,
> unison, major 2nd and mayor third's ideal representations are not
> equally spaced, so the diatonic structure gets a little weird, if
> not impossible to handle in a standard way. in 31-edo, however, you
> get CDEFGAB's renderings as 0-5-10-13-18-23-28 31-edo steps.

Which is the entire point if you want to talk to traditionalists.

> It is not that you can't compose diatonic stuff in 22-edo, nor that
> 31-edo's approach can't be other than diatonic.

There's a question of what diatonic even means in 22; I can think of
two different scales which both have a claim to being diatonic major.

🔗Maximiliano G. Miranda Zanetti <giordanobruno76@yahoo.com.ar>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
...
> > One point of 31-edo against, say, 22-edo, is that the diatonic
> > structure CDEFGAB can be straightforwardly defined: In 22-edo,
> > unison, major 2nd and mayor third's ideal representations are
not
> > equally spaced, so the diatonic structure gets a little weird,
if
> > not impossible to handle in a standard way. in 31-edo, however,
you
> > get CDEFGAB's renderings as 0-5-10-13-18-23-28 31-edo steps.
>

> Which is the entire point if you want to talk to traditionalists.

Hum... I guess you got lost in the message thread. This had been
taken from a previous message in which I aimed at answering Yahya's
question (what a diesis is, what enharmonic equivalence is like in
31-edo, etc.).

I don't consider Yahya a traditionalist. If he disagrees, he may
want to make a statement about it. :D

Cordially
Max.

PS:
> There's a question of what diatonic even means in 22; I can think
of
> two different scales which both have a claim to being diatonic
major.

Yeah; having read one of Erlich's interesting papers on the issue, I
am aware of that. That's my point. The complex task of translating
diatonicity from 12- to 22-edo.